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Multi-wavelength combination source with fringe pattern transform technique to reduce the equivalent coherence length in white light interferometry
Sensors and Actuators 84 Ž2000. 7–10 www.elsevier.nlrlocatersna
Multi-wavelength combination source with fringe pattern transform technique to reduce the equivalent coherence length in white light interferometry D.N. Wang ) Department of Electrical Engineering, The Hong Kong Polytechnic UniÕersity, Hung Hom, Kowloon, Hong Kong, People’s Republic of China Accepted 4 December 1999
Abstract Coherence length is one of the key factors to determine the measurement resolution in white light interferometry. By the use of multi-wavelength combination source, the equivalent coherence length can be greatly reduced. In this work, the multi-wavelength combination source together with the fringe pattern transform technique is used to further reduce the equivalent coherence length and achieve a stable, high precision white light interferometric measurement. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Multi-wavelength combination source; Fringe pattern transform; Equivalent coherence length; White light interferometry
1. Introduction White light interferometry has been an efficient technique to increase the unambiguous measurement range and perform remote and absolute measurement w1,2x. The fringe pattern obtained from a white light interferometer consists of a series of sinusoidal oscillations with a slowly varying envelope. When the interferometer is illuminated by a multi-mode laser diode, the fringe envelope can be represented by a Gaussian function w3x. In order to perform a high-precision measurement, the central fringe in the output white light fringe pattern has to be accurately determined, as it corresponds to the zero optical path difference ŽOPD. position that provides a reliable reference for the measurement. However, due to the flat shape of Gaussian function near the central fringe position, the intensity difference between the central fringe and its side fringes is very small, which creates a great difficulty in pursuing a high precision measurement. In the recent efforts, two wavelength and multi-wavelength combination source techniques have been developed and become powerful
)
Tel.: q852-27666163; fax: q852-23301544. E-mail address: [email protected] ŽD.N. Wang.
tools for central fringe identification w4–6x. On the other hand, a key factor to determine the measurement resolution in white light interferometry is the coherence length of the light source used. When the light source possesses a short coherence length, an accurate measurement can be readily achieved. A commonly used white light source, such as an LED or a multi-mode laser diode, usually exhibits a coherence length of about tens of micrometers, which to some extent, limits the measurement resolution. The output fringe pattern from a two-wavelength combination source consists of a series of fringe packets. The equivalent coherence length of such a source may be defined as the full width of the central fringe packet when the envelope of the fringe has fallen to 1re of the peak value, usually about a few micrometers. In the case of multi-wavelength combination source, the central fringe becomes dominant, and the corresponding equivalent coherence length may be defined as the full-width-half-maximum ŽFWHM. value of the central fringe amplitude, typically less than one micrometer. In order to further reduce the equivalent coherence length, a fringe pattern transform technique has been explored w7x, which makes a discrete fringe pattern appear in the interferometer output, with an extremely dominant and narrow central fringe, hence, reducing the equivalent coherence length to a sub-micrometer level. However, for the single wavelength source, the
0924-4247r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 9 9 . 0 0 3 5 4 - 4
D.N. Wang r Sensors and Actuators 84 (2000) 7–10
8
original fringe pattern exhibits only small intensity difference between the central fringe and its side fringes and as a result, the central fringe may shift to its side fringe position occasionally. Such a system possesses low stability unless efficient time average scheme is employed, which in turn, increases the signal processing time and system complexity. On the contrary, by the use of multiwavelength combination source, the central fringe is dominant in the original fringe pattern, a highly stable output thus can be realized when performing discrete fringe pattern transform. In this paper, the fringe pattern from a multi-wavelength combination source consisting of three commonly used multi-mode laser diodes is transformed into a discrete fringe pattern. The output is highly stable, without any central fringe shift. Such a source is particularly suitable for high precision white light interferometric measurement where good system stability is critically required.
2. Principle of operation For a multi-wavelength combination source consisting of three laser diodes of wavelength l1 , l2 and l3 , respectively, and of coherence length L c1 , L c2 and Lc3 , respectively, the normalized ac signal intensity can be expressed as: 2
½
i Ž x . s Ž 1r3 . exp y Ž 2 xrLc1 . cos Ž 2p xrl1 . 2
qexp y Ž 2 xrLc2 . cos Ž 2p xrl2 . 2
qexp y Ž 2 xrLc3 . cos Ž 2p xrl3 .
5
Ž 1.
where x is the OPD introduced by the interferometer. When three laser diodes chosen are LD1 Ž l1 s 635 nm, Lc1 s 16 mm., LD2 Ž l2 s 786 nm, Lc2 s 35 mm. and LD3 Ž l3 s 830 nm, Lc3 s 15 mm., respectively, the normalized output fringe pattern can be generated by computer simulations and is shown in Fig. 1Ža.. It can be observed from this figure that the central fringe is dominant and has a large intensity difference with all its side fringes. In order to increase further the intensity difference between the central fringe and its side fringes and reduce the equivalent coherence length of the light source, the discrete fringe patter transform i n s Ž 1r2 . i Ž x . q i 2 Ž x .
4
n
Fig. 1. Computer simulated multi-wavelength combination source fringe patterns. Ž l1 s635 nm, Lc1 s16 mm, l2 s 786 nm, L c2 s 35 mm, l3 s830 nm and Lc3 s15 mm.. Ža. Original signal, iŽ x .; Žb. i1Ž x . s w iŽ x .q iŽ x . 2 xr2; Žc. i 2 Ž x . s w iŽ x .q iŽ x . 2 xr24 2 ; Žd. i 4 Ž x . s w iŽ x .q iŽ x . 2 xr244 .
Ž 2.
is introduced to the system and the results are shown in Fig. 1Žb., Žc. and Žd., corresponding to the transform stage n s 1, 2 and 4, respectively. The FWHM values of the
central fringe amplitude, i.e., the equivalent coherence length, are 240, 200, 160 and 120 nm, respectively, corresponding to the original fringe pattern, the fringe pattern with transform stage n s 1, 2 and 4, respectively. As
D.N. Wang r Sensors and Actuators 84 (2000) 7–10
9
three wavelengths are l1 s 635 nm, l2 s 786 nm and l3 s 830 nm, respectively, and the corresponding coherence lengths are Lc1 s 16 mm, Lc2 s 35 mm and Lc3 s 15 mm, respectively. A set of fringe patterns obtained at different transform stages is shown in Fig. 4. Fig. 4Ža. shows the original
Fig. 2. Equivalent coherence length vs. signal transform stage n.
shown by the theoretical curve in Fig. 2, a progressive reduction of equivalent coherence length can be achieved.
3. Experimental results The experimental arrangement used for fringe pattern transform is shown in Fig. 3. The outputs from three typical commercially available laser diodes were first combined by the use of two beam splitters to produce a single light beam to illuminate a balanced Michelson interferometer. The two output beams from the interferometer, reflected by mirror M1 and M2, respectively, were detected by a photodetector. The interference pattern was generated by modulating the OPD via an electromechanical modulation of the position of one of the mirrors, M1, and the output was recorded with a personal computer, through a digital storage adapter connected to an oscilloscope. The fringe pattern transform was carried out by the use of a simple computer program. The three laser diodes were all operated below their threshold in order to ensure the multi-mode nature of the output and hence the fringe pattern obtained could be observed more easily on the oscilloscope. The laser diodes used in the experiment were similar to those employed in computer simulations, i.e., the
Fig. 3. Schematic diagram of experimental arrangement.
Fig. 4. Experimentally obtained fringe patterns. Ž l1 s635 nm, Lc1 s16 mm, l 2 s 786 nm, Lc2 s 35 mm, l3 s830 nm and Lc3 s15 mm.. Ža. Original signal, iŽ x .; Žb. i1Ž x . s w iŽ x .q iŽ x . 2 xr2; Žc. i 2 Ž x . s w iŽ x .q iŽ x . 2 xr24 2 ; Žd. i 4 Ž x . s w iŽ x .q iŽ x . 2 xr244 .
10
D.N. Wang r Sensors and Actuators 84 (2000) 7–10
fringe pattern, Fig. 4Žb. represents the fringe pattern when n s 1 and Fig. 4Žc. and Žd. demonstrate the fringe patterns when n s 2 and n s 4, respectively. These fringe patterns are in good agreement with those obtained in the computer simulations, thus, verifying the reliability of the technique. The asymmetry appears in the fringe pattern may be caused by the misalignment of the system or the dispersion element used in the interferometer w8x. The experimentally obtained values of equivalent coherence length at each fringe pattern transform stage are also shown in Fig. 2. A close match can be found when these values are compared with the theoretical curve.
4. Discussion By the use of discrete fringe pattern transform technique to perform high precision measurement, stability is one of the major concerns when the system operates in a noisy environment. The multi-wavelength combination source is particularly suitable for such an application as the large intensity difference between the central fringe and its side fringes can ensure a stable output. Although the system alignment difficulty may arise and some means of dispersion compensation may need to be adopted, the multi-wavelength combination source system is robust and can operate without any additional time average signal processing. In addition, when compared with the fringe pattern transform with a single wavelength source, the multi-wavelength combination source needs only smaller number of transform stages to obtain a similar intensity
difference between the central fringe and its side fringes. In conclusion, multi-wavelength combination source together with the discrete fringe pattern transform technique provides a reliable means to reduce the equivalent coherence length, the system is robust and possesses high potential to improve measurement resolution in white light interferometry.
References w1x T. Bosselman, R. Ulrich, High accuracy position-sensing with fiber coupled white light interferometers, in: Proc. 2nd OFS Conf., Stuttgart, Germany,1984, pp. 361–365. w2x A. Koch, R. Ulrich, Fiber-optic displacement sensor with 0.02 mm resolution by white-light interferometry, Sensors and Actuators A 25–27 Ž1991. 201–207. w3x W.V. Etten, J.V.D. Plaats, in: Fundamentals of Optical Fiber Communications,1991, p. 153, Prentice-Hall. w4x S. Chen, K.T.V. Grattan, B.T. Meggitt, A.W. Palmer, Instantaneous fringe-order identification using dual broad-band sources with widely spaced wavelengths, Electron. Lett. 29 Ž1993. 334–335. w5x Y.J. Rao, D.A. Jackson, Synthesized source for white-light sensing systems, Opt. Lett. 18 Ž1993. 462–464. w6x D.N. Wang, Y.N. Ning, K.T.V. Grattan, A.W. Palmer, K. Weir, Three wavelength combination source for white-light interferometry, IEEE Photonics Technol. Lett. 5 Ž1993. 1350–1352. w7x D.N. Wang, C. Shu, Discrete fringe pattern to reduce the resolution limit for white light interferometry, Opt. Commun. 162 Ž1999. 187– 190. w8x D.N. Wang, K.T.V. Grattan, A.W. Palmer, Dispersion effect analysis with multiwavelength combination sources in optical sensor applications, Opt. Commun. 127 Ž1996. 19–24.
Multi-wavelength combination source with fringe pattern transform technique to reduce the equivalent coherence length in white light interferometry D.N. Wang ) Department of Electrical Engineering, The Hong Kong Polytechnic UniÕersity, Hung Hom, Kowloon, Hong Kong, People’s Republic of China Accepted 4 December 1999
Abstract Coherence length is one of the key factors to determine the measurement resolution in white light interferometry. By the use of multi-wavelength combination source, the equivalent coherence length can be greatly reduced. In this work, the multi-wavelength combination source together with the fringe pattern transform technique is used to further reduce the equivalent coherence length and achieve a stable, high precision white light interferometric measurement. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Multi-wavelength combination source; Fringe pattern transform; Equivalent coherence length; White light interferometry
1. Introduction White light interferometry has been an efficient technique to increase the unambiguous measurement range and perform remote and absolute measurement w1,2x. The fringe pattern obtained from a white light interferometer consists of a series of sinusoidal oscillations with a slowly varying envelope. When the interferometer is illuminated by a multi-mode laser diode, the fringe envelope can be represented by a Gaussian function w3x. In order to perform a high-precision measurement, the central fringe in the output white light fringe pattern has to be accurately determined, as it corresponds to the zero optical path difference ŽOPD. position that provides a reliable reference for the measurement. However, due to the flat shape of Gaussian function near the central fringe position, the intensity difference between the central fringe and its side fringes is very small, which creates a great difficulty in pursuing a high precision measurement. In the recent efforts, two wavelength and multi-wavelength combination source techniques have been developed and become powerful
)
Tel.: q852-27666163; fax: q852-23301544. E-mail address: [email protected] ŽD.N. Wang.
tools for central fringe identification w4–6x. On the other hand, a key factor to determine the measurement resolution in white light interferometry is the coherence length of the light source used. When the light source possesses a short coherence length, an accurate measurement can be readily achieved. A commonly used white light source, such as an LED or a multi-mode laser diode, usually exhibits a coherence length of about tens of micrometers, which to some extent, limits the measurement resolution. The output fringe pattern from a two-wavelength combination source consists of a series of fringe packets. The equivalent coherence length of such a source may be defined as the full width of the central fringe packet when the envelope of the fringe has fallen to 1re of the peak value, usually about a few micrometers. In the case of multi-wavelength combination source, the central fringe becomes dominant, and the corresponding equivalent coherence length may be defined as the full-width-half-maximum ŽFWHM. value of the central fringe amplitude, typically less than one micrometer. In order to further reduce the equivalent coherence length, a fringe pattern transform technique has been explored w7x, which makes a discrete fringe pattern appear in the interferometer output, with an extremely dominant and narrow central fringe, hence, reducing the equivalent coherence length to a sub-micrometer level. However, for the single wavelength source, the
0924-4247r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 9 9 . 0 0 3 5 4 - 4
D.N. Wang r Sensors and Actuators 84 (2000) 7–10
8
original fringe pattern exhibits only small intensity difference between the central fringe and its side fringes and as a result, the central fringe may shift to its side fringe position occasionally. Such a system possesses low stability unless efficient time average scheme is employed, which in turn, increases the signal processing time and system complexity. On the contrary, by the use of multiwavelength combination source, the central fringe is dominant in the original fringe pattern, a highly stable output thus can be realized when performing discrete fringe pattern transform. In this paper, the fringe pattern from a multi-wavelength combination source consisting of three commonly used multi-mode laser diodes is transformed into a discrete fringe pattern. The output is highly stable, without any central fringe shift. Such a source is particularly suitable for high precision white light interferometric measurement where good system stability is critically required.
2. Principle of operation For a multi-wavelength combination source consisting of three laser diodes of wavelength l1 , l2 and l3 , respectively, and of coherence length L c1 , L c2 and Lc3 , respectively, the normalized ac signal intensity can be expressed as: 2
½
i Ž x . s Ž 1r3 . exp y Ž 2 xrLc1 . cos Ž 2p xrl1 . 2
qexp y Ž 2 xrLc2 . cos Ž 2p xrl2 . 2
qexp y Ž 2 xrLc3 . cos Ž 2p xrl3 .
5
Ž 1.
where x is the OPD introduced by the interferometer. When three laser diodes chosen are LD1 Ž l1 s 635 nm, Lc1 s 16 mm., LD2 Ž l2 s 786 nm, Lc2 s 35 mm. and LD3 Ž l3 s 830 nm, Lc3 s 15 mm., respectively, the normalized output fringe pattern can be generated by computer simulations and is shown in Fig. 1Ža.. It can be observed from this figure that the central fringe is dominant and has a large intensity difference with all its side fringes. In order to increase further the intensity difference between the central fringe and its side fringes and reduce the equivalent coherence length of the light source, the discrete fringe patter transform i n s Ž 1r2 . i Ž x . q i 2 Ž x .
4
n
Fig. 1. Computer simulated multi-wavelength combination source fringe patterns. Ž l1 s635 nm, Lc1 s16 mm, l2 s 786 nm, L c2 s 35 mm, l3 s830 nm and Lc3 s15 mm.. Ža. Original signal, iŽ x .; Žb. i1Ž x . s w iŽ x .q iŽ x . 2 xr2; Žc. i 2 Ž x . s w iŽ x .q iŽ x . 2 xr24 2 ; Žd. i 4 Ž x . s w iŽ x .q iŽ x . 2 xr244 .
Ž 2.
is introduced to the system and the results are shown in Fig. 1Žb., Žc. and Žd., corresponding to the transform stage n s 1, 2 and 4, respectively. The FWHM values of the
central fringe amplitude, i.e., the equivalent coherence length, are 240, 200, 160 and 120 nm, respectively, corresponding to the original fringe pattern, the fringe pattern with transform stage n s 1, 2 and 4, respectively. As
D.N. Wang r Sensors and Actuators 84 (2000) 7–10
9
three wavelengths are l1 s 635 nm, l2 s 786 nm and l3 s 830 nm, respectively, and the corresponding coherence lengths are Lc1 s 16 mm, Lc2 s 35 mm and Lc3 s 15 mm, respectively. A set of fringe patterns obtained at different transform stages is shown in Fig. 4. Fig. 4Ža. shows the original
Fig. 2. Equivalent coherence length vs. signal transform stage n.
shown by the theoretical curve in Fig. 2, a progressive reduction of equivalent coherence length can be achieved.
3. Experimental results The experimental arrangement used for fringe pattern transform is shown in Fig. 3. The outputs from three typical commercially available laser diodes were first combined by the use of two beam splitters to produce a single light beam to illuminate a balanced Michelson interferometer. The two output beams from the interferometer, reflected by mirror M1 and M2, respectively, were detected by a photodetector. The interference pattern was generated by modulating the OPD via an electromechanical modulation of the position of one of the mirrors, M1, and the output was recorded with a personal computer, through a digital storage adapter connected to an oscilloscope. The fringe pattern transform was carried out by the use of a simple computer program. The three laser diodes were all operated below their threshold in order to ensure the multi-mode nature of the output and hence the fringe pattern obtained could be observed more easily on the oscilloscope. The laser diodes used in the experiment were similar to those employed in computer simulations, i.e., the
Fig. 3. Schematic diagram of experimental arrangement.
Fig. 4. Experimentally obtained fringe patterns. Ž l1 s635 nm, Lc1 s16 mm, l 2 s 786 nm, Lc2 s 35 mm, l3 s830 nm and Lc3 s15 mm.. Ža. Original signal, iŽ x .; Žb. i1Ž x . s w iŽ x .q iŽ x . 2 xr2; Žc. i 2 Ž x . s w iŽ x .q iŽ x . 2 xr24 2 ; Žd. i 4 Ž x . s w iŽ x .q iŽ x . 2 xr244 .
10
D.N. Wang r Sensors and Actuators 84 (2000) 7–10
fringe pattern, Fig. 4Žb. represents the fringe pattern when n s 1 and Fig. 4Žc. and Žd. demonstrate the fringe patterns when n s 2 and n s 4, respectively. These fringe patterns are in good agreement with those obtained in the computer simulations, thus, verifying the reliability of the technique. The asymmetry appears in the fringe pattern may be caused by the misalignment of the system or the dispersion element used in the interferometer w8x. The experimentally obtained values of equivalent coherence length at each fringe pattern transform stage are also shown in Fig. 2. A close match can be found when these values are compared with the theoretical curve.
4. Discussion By the use of discrete fringe pattern transform technique to perform high precision measurement, stability is one of the major concerns when the system operates in a noisy environment. The multi-wavelength combination source is particularly suitable for such an application as the large intensity difference between the central fringe and its side fringes can ensure a stable output. Although the system alignment difficulty may arise and some means of dispersion compensation may need to be adopted, the multi-wavelength combination source system is robust and can operate without any additional time average signal processing. In addition, when compared with the fringe pattern transform with a single wavelength source, the multi-wavelength combination source needs only smaller number of transform stages to obtain a similar intensity
difference between the central fringe and its side fringes. In conclusion, multi-wavelength combination source together with the discrete fringe pattern transform technique provides a reliable means to reduce the equivalent coherence length, the system is robust and possesses high potential to improve measurement resolution in white light interferometry.
References w1x T. Bosselman, R. Ulrich, High accuracy position-sensing with fiber coupled white light interferometers, in: Proc. 2nd OFS Conf., Stuttgart, Germany,1984, pp. 361–365. w2x A. Koch, R. Ulrich, Fiber-optic displacement sensor with 0.02 mm resolution by white-light interferometry, Sensors and Actuators A 25–27 Ž1991. 201–207. w3x W.V. Etten, J.V.D. Plaats, in: Fundamentals of Optical Fiber Communications,1991, p. 153, Prentice-Hall. w4x S. Chen, K.T.V. Grattan, B.T. Meggitt, A.W. Palmer, Instantaneous fringe-order identification using dual broad-band sources with widely spaced wavelengths, Electron. Lett. 29 Ž1993. 334–335. w5x Y.J. Rao, D.A. Jackson, Synthesized source for white-light sensing systems, Opt. Lett. 18 Ž1993. 462–464. w6x D.N. Wang, Y.N. Ning, K.T.V. Grattan, A.W. Palmer, K. Weir, Three wavelength combination source for white-light interferometry, IEEE Photonics Technol. Lett. 5 Ž1993. 1350–1352. w7x D.N. Wang, C. Shu, Discrete fringe pattern to reduce the resolution limit for white light interferometry, Opt. Commun. 162 Ž1999. 187– 190. w8x D.N. Wang, K.T.V. Grattan, A.W. Palmer, Dispersion effect analysis with multiwavelength combination sources in optical sensor applications, Opt. Commun. 127 Ž1996. 19–24.